The authors relax the closeness-to-identity condition in Assumption (B) of Gusakova et al. so that central and stable limit theorems for simplex volumes hold under spiked and Toeplitz covariance structures.
High Dimensional Statistical Inference and Random Matrices
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abstract
Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier half of the last century. Subsequently, random matrix theory (RMT) developed, initially within physics, and more recently widely in mathematics. While some of the central objects of study in RMT are identical to those of multivariate statistics, statistical theory was slow to exploit the connection. However, with vast data collection ever more common, data sets now often have as many or more variables than the number of individuals observed. In such contexts, the techniques and results of RMT have much to offer multivariate statistics. The paper reviews some of the progress to date.
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A note on "The volume of random simplices from elliptical distributions in high dimension"
The authors relax the closeness-to-identity condition in Assumption (B) of Gusakova et al. so that central and stable limit theorems for simplex volumes hold under spiked and Toeplitz covariance structures.